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  1. Home
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  3. Infinite Electrical Networks
  • Cited by 48
Publisher:
Cambridge University Press
Online publication date:
February 2012
Print publication year:
1991
Online ISBN:
9780511895432
DOI:
https://doi.org/10.1017/CBO9780511895432
Subjects:
Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Discrete Mathematics Information Theory and Coding
Series:
Cambridge Tracts in Mathematics (101)
Information

Book description

This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition. Using the basic tools of functional analysis and graph theory, the author examines the fundamental developments in the field and discusses applications to other areas of mathematics. The first half of the book presents existence and uniqueness theorems for both infinite-power and finite-power voltage-current regimes, and the second half discusses methods for solving problems in infinite cascades and grids. A notable feature is the invention of transfinite networks, roughly analogous to Cantor's extension of the natural numbers to the transfinite ordinals. The last chapter is a survey of application to exterior problems of partial differential equations, random walks on infinite graphs, and networks of operators on Hilbert spaces.

Reviews

"...The book would make a fine Graduate level text for Electrical Engineers; it would also be useful for students in applied mathematics as a guide to possible research topics." Andrew Booth, Physics in Canada

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